Which version of PSP is it?
If it's sufficiently recent, you can use a special cable to send output from the PSP to a nice widescreen TV.
I picked one up a couple years back and it's been excellent for UMD videos and games where a slightly bigger screen and sound system (yeah, I'm looking at you Rock Band!) can be helpful.
Anyway, point being this: If you can output to a TV screen, then you know that at least the PSP is generating a solid video signal. So if it's not the screen itself (already replaced you said) and it's not simply a "brightness level" thing (I assume you've futzed with the buttons) and if the cable works then obviously it's the connection between the screen and the video signal.